Two airlines, Dragon Airline and Phoenix Airline, provide direct flight service to a city and tend to compete for the same group of travellers. They are contemplating changing their airfares to earn more profit. If both airlines raise their airfares, Dragon Airline will earn $800m while Phoenix Airline will earn $400m in profit. If both airlines reduce their airfares, Dragon Airline will earn $650m while Phoenix Airline will earn $550m in profit. If Dragon Airline raises its airfare while Phoenix Airline reduces its airfare, Dragon Airline will earn $200m while Phoenix Airline will earn $350m in profit. If Dragon Airline reduces its airfare while Phoenix Airline raises its airfare, Dragon Airline will earn $300m while Phoenix Airline will earn $250m in profit. Construct the payoff matrix in terms of profit for the two pricing strategies. Apply a game theory concept and solve this game using the Nash equilibrium method. Explain how you derive your answers and also whether this game is a prisoner's dilemma game. How will your answer be different if the game become a sequential game and Phoenix Airline gets to move first? Explain your answers by constructing a suitable decision tree diagram, employ the roll back method